WASHINGTON — The election laid bare a dual — and dueling — nation, politically speaking, jaggedly split down the middle on the presidency and torn over much else. It seems you can please only half of the people nearly all of the time.

Americans retained the fractious balance of power in re-electing President Barack Obama, a Republican House and a Democratic Senate, altogether serving as guarantors of the gridlock that voters say they despise. Slender percentages separated winner and loser from battleground to battleground, and people in exit polls said yea and nay in roughly equal measure to some of the big issues of the day.

Democracy doesn’t care if you win big, only that you win. Tuesday was a day of decision as firmly as if Obama had run away with the race. Democrats are ebullient and, after a campaign notable for its raw smackdowns, words of conciliation are coming from leaders on both sides, starting with the plea from defeated Republican rival Mitt Romney that his crestfallen supporters pray for the president.

But after the most ideologically polarized election in years, Obama’s assertion Wednesday morning that America is “more than a collection of red states and blue states” was more of an aspiration than a snapshot of where the country stands.

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“It’s going to take a while for this thing to heal,” said Ron Bella, 59, a Cincinnati lawyer who lives in Alexandria, Ky. He is relieved Obama won, but some of his co-workers are in a “sour mood” about it.

“They feel like the vast majority of the country wanted Romney, and the East and the West coasts wanted Obama,” he said. “I’m not sure exactly why that is, but there just seems to be such hatred for Obama out there.”

Compromise was a popular notion in the hours after Obama’s victory and an unavoidable one, given the reality of divided government. But the familiar contours of partisan Washington were also in evidence, especially the notion that compromise means you do things my way.

As Democratic Rep. Steve Israel of New York put it, “If you refuse to compromise, we are going to beat you.” Israel, chairman of the Democratic Congressional Campaign Committee, said the election showed “if you are an extremist tea party Republican, you are going to lose.”

Senate Republican Leader Mitch McConnell of Kentucky said pointedly that Republicans will meet Obama halfway “to the extent he wants to move to the political center” and propose solutions “that actually have a chance of passing.”

In New York’s bustling Times Square, hope, skepticism and the usual polarities were all to be found when people talked about the president. “He may not have done a great job in my mind but I kinda trust him,” said Jerry Shul. “I have faith he will get with the Republicans and get something done.”

A less-flattering George Dallemand called this “a moment of truth” for the country. “I guess we have to wish for the best now, but I still think he is socialism.”

In Miami, Karen Fitzgerald, 55, wore a black dress and said she was in mourning over Romney’s defeat.

“It’s an upsetting day,” she said. But she took some comfort from her Democratic friends on Facebook, who have stopped chiding the other side in their posts. “Now they’re all saying we need to work together and be united,” she said. “Maybe we can.”

In Springfield, Ohio, an “elated” Frank Hocker, 67, hoped Republicans would get the message to get out of Obama’s way. “There was a backlash,” he said. “For this obstructionist House and those tea party people, I hope they learned their lesson. I hope they learned their lesson: Don’t stop the progress of this country.”

In Chicago, Obama supporter Scherita Parrish, 56, predicted the president will reach out to Republicans but may not get much back.

“But the people have spoken,” she said. “They need to lick their wounds, get on with it and start working with the president.”

Unity is a challenge not just for Obama but for the Republicans, who won less than 30 percent of the growing Hispanic vote and not even one in 10 black voters. Obama built a strong Electoral College majority, if only a narrow advantage in the popular vote, despite losing every age group of non-Hispanic white voters.

Surveys of voters found Obama’s health care law to be as divisive as ever, with just under 50 percent wanting it repealed in whole or part, and 44 percent liking it as is or wanting more of it.

But democracy doesn’t care about exit polls, either, and the election almost certainly means Republicans can forget about trying to roll it back now.

In reaffirming divided government, though, Americans all but ensured colossal fights are ahead over the shape of government and Obama’s agenda. He is out to break a wall of Republican opposition to tax increases on the wealthy — a move that about half the voters in exit polls thought was a good idea. And extraordinarily difficult negotiations are imminent as the president and Congress try to make a deal to avoid the “fiscal cliff” — steep spending cuts and a variety of tax increases in January.

In the end, voters split about equally on whether Obama or Romney would be better at handling the economy.

Then again, they were divided down the middle on whether Obama or his predecessor, George W. Bush, deserves most of the blame for the economy’s problems.